Nadal, who lost his number world one ranking after his 14-match winning run on clay was snapped by Thiem in the Madrid Open quarter-finals last week, was back to his best as he wrapped up victory with a blistering forehand winner.
"It was important, after a loss in Madrid, to come back strong," the 31-year-old, who received a bye in the opening round, said. "And that's what I did today.
"I went on court with the right intensity. I don't know how many mistakes I made, but not many. I also had control, more or less, of a high percentage of the points. That was the way that I want to play."
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The Spaniard can reclaim the world number one ranking from Roger Federer if he wins a record-extending eighth title in Rome this week.
Thiem, who finished runner-up in Madrid on Sunday, struggled to find his rhythm in a 6-4 1-6 6-3 defeat by Fabio Fognini.
World number 21 Fognini, backed by a partisan Italian crowd, frustrated Thiem with well-placed lobs and touch volleys and went on to record his first win over the Austrian in three meetings.
Novak Djokovic, a four-time winner in Rome, powered into the third round with a convincing 6-4 6-2 win over Georgian Nikoloz Basilashvili.
The Serb will have opportunity to reach his first quarter-final of the season on Thursday, when he faces Spain's Albert Ramos-Vinolas.
Japan's Kei Nishikori denied Grigor Dimitrov a 27th birthday win to progress to the third round, rallying back from a set down to beat the world number four 6-7(4) 7-5 6-4.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
